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一类强交错扩散的捕食模型弱解的整体存在性

李慧玲

李慧玲. 一类强交错扩散的捕食模型弱解的整体存在性[J]. 应用数学和力学, 2009, 30(6): 677-689. doi: 10.3879/j.issn.1000-0887.2009.06.007
引用本文: 李慧玲. 一类强交错扩散的捕食模型弱解的整体存在性[J]. 应用数学和力学, 2009, 30(6): 677-689. doi: 10.3879/j.issn.1000-0887.2009.06.007
LI Hui-ling. Global Existence of Weak Solutions to a Prey-Predator Model With Strong Cross-Diffusion[J]. Applied Mathematics and Mechanics, 2009, 30(6): 677-689. doi: 10.3879/j.issn.1000-0887.2009.06.007
Citation: LI Hui-ling. Global Existence of Weak Solutions to a Prey-Predator Model With Strong Cross-Diffusion[J]. Applied Mathematics and Mechanics, 2009, 30(6): 677-689. doi: 10.3879/j.issn.1000-0887.2009.06.007

一类强交错扩散的捕食模型弱解的整体存在性

doi: 10.3879/j.issn.1000-0887.2009.06.007
基金项目: 国家自然科学基金资助项目(10701024;10601011)
详细信息
    作者简介:

    李慧玲(1977- ),女,湖南人,讲师,博士(E-mail:lihuiling_seu@yahoo.com.cn).

  • 中图分类号: O175.26

Global Existence of Weak Solutions to a Prey-Predator Model With Strong Cross-Diffusion

  • 摘要: 考虑一类带有强交错扩散项的捕食模型解的整体存在性.借助于有限差分方法和熵不等式的相关性质及结论,证明了在高维空间上,该问题有整体存在的弱解.此外,还说明了所得的这个弱解是非负解.
  • [1] Mimura M,Kawasaki K.Spatial segregation in competitive interaction-diffusion equations[J].J Math Biol,1980,9(1):49-64. doi: 10.1007/BF00276035
    [2] Shigesada N,Kawasaki K,Teramoto E.Spatial segregation of interacting species[J].J Theor Biol,1979,79(1):83-99. doi: 10.1016/0022-5193(79)90258-3
    [3] Kuto K,Yamada Y.Multiple coexistence states for a prey-predator system with cross-diffusion[J].J Diff Equns,2004,197(2):315-348. doi: 10.1016/j.jde.2003.08.003
    [4] Okubo A, Levin L A.Diffusion and Ecological Problems:Modern Perspective[M].Interdisciplinary Applied Mathematics,2nd Edition,Vol. 14. New York:Springer,2001.
    [5] Amann H.Dynamic theory of quasilinear parabolic equations Ⅱ:reaction-diffusion systems[J].Differential Integral Equations,1990,3(1):13-75.
    [6] Amann H.Dynamic theory of quasilinear parabolic equations III:Global existence[J].Math Z,1989,202(2):219-250. doi: 10.1007/BF01215256
    [7] Choi Y S,Lui R,Yamada Y.Existence of global solutions for the Shigesada-Kawasaki-Teramoto model with weak cross-diffusion[J].Discrete Contin Dynam Systems,2003,9(5):1193-1200. doi: 10.3934/dcds.2003.9.1193
    [8] Choi Y S,Lui R,Yamada Y.Existence of global solutions for the Shigesada-Kawasaki-Teramoto model with strongly coupled cross-diffusion[J].Discrete Contin Dynam Systems,2004,10(3):719-730. doi: 10.3934/dcds.2004.10.719
    [9] LOU Yuan,NI Wei-ming,WU Ya-ping.On the global existence of a cross-diffusion system[J].Discrete Contin Dynam Systems,1998,4(2):193-203. doi: 10.3934/dcds.1998.4.193
    [10] Pang P Y H ,WANG Ming-xin.Existence of global solutions for a three-species predator-prey model with cross-diffusion[J]. Mathematische Nachrichten,2008,281(4):555-560. doi: 10.1002/mana.200510624
    [11] Shim S A.Uniform boundedness and convergence of solutions to the systems with a single nonzero cross-diffusion[J].J Math Anal Appl,2003,279(1):1-21. doi: 10.1016/S0022-247X(03)00045-3
    [12] WU Ya-ping.Qualitative studies of solutions for some cross-diffusion systems[A].In:Li T T,Mimura M,Nishiura Y,et al,Eds.China-Japan Symposium on Reaction-Diffusion Equations and Their Applications and Computational Aspects[C]. Singapore:World Scientific,1997,177-187.
    [13] Knies S.Schwache lsungen von halbleitergleichungen im falle von ladungstransport mit streueffekten[D]. Germany:Universitt Bonn,1997.
    [14] CHEN Li,Jüngel A.Analysis of a multidimensional parabolic population model withstrong cross-diffusion[J].SIAM J Math Anal,2004,36(1):301-322. doi: 10.1137/S0036141003427798
    [15] CHEN Xin-fu,QI Yuan-wei,WANG Ming-xin.A strongly coupled predator-prey system with non-monotonic functional response[J].Nonlinear Anal TMA,2007,67(6):1966-1979. doi: 10.1016/j.na.2006.08.022
    [16] CHEN Xin-fu,QI Yuan-wei,WANG Ming-xin.Steady states of a strongly coupled prey-predator model[J].Discrete Contin Dynam Systems,2005,(suppl):173-180.
    [17] Pao C V.Strongly coupled elliptic systems and applications to Lotka-Volterra models with cross diffusion[J].Nonlinear Anal TMA,2005,60(7):1197-1217. doi: 10.1016/j.na.2004.10.008
    [18] Pang P Y H,WANG Ming-xin.Strategy and stationary pattern in a three-species predator-prey model[J].J Differential Equations,2004,200(2):245-273. doi: 10.1016/j.jde.2004.01.004
    [19] Ryu K,Ahn I.Positive solutions for ratio-dependent predator-prey interaction systems[J].J Differential Equations,2005,218(1):117-135. doi: 10.1016/j.jde.2005.06.020
    [20] WANG Ming-xin.Stationary patterns of strongly coupled prey-predator models[J].J Math Anal Appl,2004,292(2):484-505. doi: 10.1016/j.jmaa.2003.12.027
    [21] Dung L.Cross diffusion systems on n spatial dimensional domains[J].Indiana Univ Math J,2002,51(3):625-643.
    [22] LOU Yuan,Martìnez S,NI Wei-ming.On 3×3 Lotka-Volterra competition systems with cross-diffusion[J].Discrete Contin Dynam Systems,2000,6(1):175-190.
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出版历程
  • 收稿日期:  2008-09-22
  • 修回日期:  2009-04-21
  • 刊出日期:  2009-06-15

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